In a display of the above mentioned kind, e.g. an electrophoretic display, light that is reflected at the reflective layer cannot escape through the substrate into air if the reflection angle θs (angle with respect to the normal of the scattering layer) is larger than the critical angle θTIR. The critical angle θTIR is given by arcsin 1/ns, where ns is the index of refraction of the substrate. Typically, light that cannot propagate into air experiences total internal reflection when it reaches the substrate-air interface. This means that a large portion, typically almost 60%, of the light is reflected back into the display. This is illustrated in FIG. 1.
Light that is reflected into the display can be reflected by the reflective layer a second time, and the fraction of light that again experiences total internal reflection can be reflected for a third time, and so on. Such recycling can limit the loss of light, but in present displays the efficiency of this process is rather low, due to diffuse reflectance Rs of the reflective layer significantly less than 1, and absorption by an electrode layer (ITO) on the substrate.
Moreover, between two backscattering events the light may travel a certain distance parallel to the display surface away from the original reflecting position. For a typical thickness of the substrate of one to a few hundred micrometers, the average traveled distance is larger than the typical pixel size of about 200 micrometer. The total amount of light that is received by a pixel thus depends on the state of neighboring pixels, i.e. the perceived brightness of a pixel depends on the state of neighboring pixels. This is called optical cross-talk and becomes more visible for higher recycling efficiencies.
For encapsulated electrophoretic displays using reflective and absorbing particles dispersed in a fluid contained in capsules, such as an E-Ink® display, Rs is typically near 70% in the white state and the externally perceived diffuse reflectance Rex of a fully white display (i.e. where all neighboring pixels are also in the white state) is only about 40%. This is marginally sufficient for monochrome displays but not enough to build a full-color display by adding color filters. Even if colored pixels are used in combination with white pixels (RGBW scheme) a color display in a fully white state will have at best only half of the brightness of the white state of a monochrome display.
For electrophoretic displays using scattering particles dispersed in an absorbing fluid contained in compartments Rex is typically about 30% and even monochrome displays have insufficient brightness.